Delta - Star transformation | Star - Delta Transformation 1

 Consider a delta system that's three corner points are A, B and C as shown in the figure. Electrical resistance of the branch between points A and B, B and C and C and A are R1, R2 and R3 respectively.

The resistance between the points A and B will be,

Now, one star system is connected to these points A, B, and C as shown in the figure. Three arms RA, RB and RC of the star system are connected with A, B and C respectively. Now if we measure the resistance value between points A and B, we will get,

Since the two systems are identical, resistance measured between terminals A and B in both systems must be equal.

Similarly, resistance between points B and C being equal in the two systems

And resistance between points C and A being equal in the two systems,

Adding equations (I), (II) and (III) we get,

Subtracting equations (I), (II) and (III) from equation (IV) we get,